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Topological Methods in Nonlinear Analysis

Some generalized nonexpansive mappings and weak normal structure
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Some generalized nonexpansive mappings and weak normal structure

Authors

  • Bożena Piątek https://orcid.org/0000-0003-1011-3044

DOI:

https://doi.org/10.12775/TMNA.2023.049

Keywords

Jaggi nonexpansive mapping, orbitally nonexpansive mapping, L-type mapping, normal structure

Abstract

We consider relations between normal structure of a Banach space and the fixed point property for various classes of generalized nonexpansive mappings under additional assumptions, such as that of continuity. In this way we answer some open questions about the behaviour of such maps.

References

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R. Engelking, General Topology, Sigma Series in Pure Mathematics, vol. 6, Heldermann, 1989.

R. Espínola, M. Japón and D. Souza, Fixed points and common fixed points for orbit-nonexpansive mappings in metric spaces, Mediterr. J. Math. 20 (2023), article 182, 17 pp.

H. Fetter and E. Llorens-Fuster, Jaggi nonexpansive mappings revisited, J. Nonlinear Convex Anal. 18 (2017), 1771–1779.

K. Goebel, Concise Course on Fixed Point Theorems, Yokohama Publishers, 2002, 187 pp.

G. Kassay, A characterization of reflexive Banach spaces with normal structure, Boll. Un. Mat. Ital. A (6) 5 (1986), 273–276.

W.A. Kirk, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly 72 (1965), 1004–1006.

W.A. Kirk and B. Sims, Handbook of Metric Fixed Point Theory, Springer Netherlands, 2011, 704 pp.

V.L. Klee, Some topological properties of convex sets, Trans. Amer. Math. Soc. 78 (1955), 30–45.

E. Llorens-Fuster, Orbitally nonexpansive mappings, Bull. Aust. Math. Soc. 93 (2016), 497–503.

E. Llorens-Fuster and E. Moreno-Gálvez, The fixed point theory for some generalized nonexpansive mappings, Abstr. Appl. Anal. 2011 (2011), article ID 435686, 15 pp.

A. Nicolae, Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits, Fixed Point Theory Appl. 2010 (2010), article ID 458265, 19 pp.

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Published

2024-03-03

How to Cite

1.
PIĄTEK, Bożena. Some generalized nonexpansive mappings and weak normal structure. Topological Methods in Nonlinear Analysis. Online. 3 March 2024. Vol. 63, no. 1, pp. 285 - 298. [Accessed 29 June 2025]. DOI 10.12775/TMNA.2023.049.
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Issue

Vol 63, No 1 (March 2024)

Section

Articles

License

Copyright (c) 2024 Bożena Piątek

Creative Commons License

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

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